This paper examines the green Schumpeterian endogenous growth model is robust. The principal findings of this paper can be summarized as follows. Firstly, diverging from the knife-edge condition typical in endogenous growth theory, the study reveals that the green Schumpeterian model exhibits dual knife-edge conditions. However, the dual knife-edge conditions are not necessary conditions for the emergence of green endogenous growth within the framework of the green Schumpeterian endogenous growth theory, showcasing the model is robust. Secondly, when the elasticity coefficients of quality innovation level and green innovation level exceed 1, the inverted U-shaped relationship between pollution emissions and green innovation level, as well as output level, persists. Thirdly, pollution emissions exhibit an inverted U-shaped trend with the reduction in the green premium. The higher the elasticity coefficients of quality innovation level and green innovation level, the greater the requirement for the green premium to reach the turning point of this curve. Lastly, reducing the green premium contributes to driving economic growth during the green innovation stage. As the elasticity coefficients of quality innovation level and green innovation level increase, the impact of reducing the green premium on promoting economic growth becomes more pronounced.

中文翻译：

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稳健的绿色熊彼特内生增长模型和空间库兹涅茨曲线

本文检验了绿色熊彼特内生增长模型的稳健性。本文的主要发现可总结如下。首先，与内生增长理论中典型的刀口条件不同，研究揭示了绿色熊彼特模型表现出双重刀口条件。然而，在绿色熊彼特内生增长理论框架内，双刀口条件并不是绿色内生增长出现的必要条件，这表明该模型是稳健的。其次，当质量创新水平和绿色创新水平的弹性系数超过1时，污染排放与绿色创新水平以及产出水平之间的倒U型关系仍然存在。第三，随着绿色溢价的下降，污染排放呈现倒U型趋势。质量创新水平和绿色创新水平的弹性系数越高，达到该曲线拐点的绿色溢价要求就越高。最后，降低绿色溢价有助于推动绿色创新阶段的经济增长。随着质量创新水平和绿色创新水平弹性系数的提高，降低绿色溢价对促进经济增长的作用更加明显。